Question

If x, y, z are in H.P. then the value of expression log (x+z) + log (x-2y + z) will be :
(A) log Ix-zl (B) 2log X-z] (C) 3 log (x-z] (D) 4log X-2

Answer 1

Answer:

2 Log |x -z|

Step-by-step explanation:

If x, y, z are in H.P. then the value of expression log (x+z) + log (x-2y + z) will be :

2/y  = 1/x + 1/z

=> 2/y = (x + z)/xz

=> y = 2xz/(x + z)

log (x+z) + log (x-2y + z)

= log (x + z)(x + z - 2y)  =  

= log {(x + z)( x + z   - 2*2xz/(x + z))}

= log {(x + z)² - 2*2xz}

= log {x² + z² + 2xz - 4xz}

=  log {x² + z² - 2xz}

=log { (x - z)²}

= 2 Log |x -z|

Answer 2

Answer:

If x, y, z are in H.P. then the value of expression log (x+z) + log (x-2y + z) will be :

2/y  = 1/x + 1/z

=> 2/y = (x + z)/xz

=> y = 2xz/(x + z)

log (x+z) + log (x-2y + z)

= log (x + z)(x + z - 2y)  =  

= log {(x + z)( x + z   - 2*2xz/(x + z))}

= log {(x + z)² - 2*2xz}

= log {x² + z² + 2xz - 4xz}

=  log {x² + z² - 2xz}

=log { (x - z)²}

= 2 Log |x -z|

Step-by-step explanation: